I had the same problem with lots of room left in my shaw mail account and running windows 10 in Chrome. The solution was to open shaw webmail, click on the "preferences" tab and then, under the "sign in" heading, click on Advanced (Ajax) instead of Standard (HTML). Save the change and restart webmail. I could then attach a Word doc with no problems. Hopefully I don't encounter other problems after making this change.
Glad you got some support, I've spent at least 6 hours on hold and had 3 different supposed techs, 2 of which I could barely understand and none of them were any help.